A good way to start is to learn some basics, such as Canon words in game used frequently. 

Ex: Krosis, Dinok, Zu'u, Yol, Fus, etc...

Basics would more likely be the Canon words, some words used in phrases and the plural form.

If you want to expand, try going for possessive suffixs and basic prefix's like "Vo-" or "Ni-".

You can also learn by our learn section which will take you step by step.

http://www.thuum.org/learn/

i think the best way to start out is getting a feel for the language by learning the Songs of Skyrim that feature Dovahzul like Sovngarde and the maintheme - that gives you quite some words and phrases to start out, a pronounciation and its entertaining